Pith Number

pith:7DR2GJZU

pith:2015:7DR2GJZU5OBEDUXMW3GCJHMMZP

not attested not anchored not stored refs pending

A Path Integral Approach to Age Dependent Branching Processes

Chris D Greenman

arxiv:1512.05431 v4 · 2015-12-17 · physics.bio-ph · math.PR · q-bio.PE

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7DR2GJZU5OBEDUXMW3GCJHMMZP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:57:44.206865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8e3a32734eb8241d2ecb6cc249d8ccbfe5e1fc6e92b471387a340885a892cbb

Aliases

arxiv: 1512.05431 · arxiv_version: 1512.05431v4 · doi: 10.48550/arxiv.1512.05431 · pith_short_12: 7DR2GJZU5OBE · pith_short_16: 7DR2GJZU5OBEDUXM · pith_short_8: 7DR2GJZU

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7DR2GJZU5OBEDUXMW3GCJHMMZP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f8e3a32734eb8241d2ecb6cc249d8ccbfe5e1fc6e92b471387a340885a892cbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15bba0a45687fc695fab641b12a35a52ceca0bb21b8b5ba1fd8c803ac8b41ea7",
    "cross_cats_sorted": [
      "math.PR",
      "q-bio.PE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.bio-ph",
    "submitted_at": "2015-12-17T01:16:38Z",
    "title_canon_sha256": "043da1f381a0ae1e8bde7fae9838002ab4ad6bae581fe35a487eca2a80a6bb95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05431",
    "kind": "arxiv",
    "version": 4
  }
}